A First-Principles Analysis of Galactic Rotation Curves within the Spacetime Compacity Theory Framework.

A First-Principles Analysis of Galactic Rotation Curves within the Spacetime Compacity Theory Framework. Robert Bruce Davis https://orcid.org/0009-0003-5058-2870 October 30, 2025 Abstract Observed galactic rotation curves remain inconsistent with both Newtonian dynamics and General Relativity (GR) unless one assumes the existence of invisible, nonbaryonic “dark matter.” Spacetime Compacity Theory (SCT) from the book ”The Compacity of Spacetime” provides an alternative explanation by introducing the concept of variable spacetime compacity, ρc(r), as a measurable field property. This short paper demonstrates that the observed velocity distributions of galaxies can be quantitatively reproduced without invoking unseen mass, establishing a physically grounded and testable reformulation of gravitational dynamics. First Principle “The universe is a matrix of spatiotemporal cells, discrete yet continuous in their arrangement, whose compacity and vortical behavior comprise every observed force and particle – A First-Principles Analysis of Galactic Rotation Curves within the Spacetime Compacity Framework.” - R.B.Davis Introduction The persistent flatness of galactic rotation curves has long challenged standard gravitational theory. Under Newtonian or relativistic frameworks, orbital velocities should decline with increasing radius according to v(r)∝1 √r,(1) yet observations consistently reveal a near-constant velocity profile v(r)≈constant for large r. (2) This discrepancy motivated the dark matter hypothesis, which attributes the additional centripetal acceleration to vast quantities of undetectable matter. Spacetime Compacity 1 Theory (SCT) from the book ”The Compacity of Spacetime” available in Kindle, offers a more parsimonious alternative: the effect arises naturally from gradients in the intrinsic compacity of spacetime itself. The Spacetime Compacity Gradient Model In SCT, spacetime is not uniform but exhibits a position-dependent compacity ρc(r), representing its internal density or compression. Changes in ρcproduce differential field stiffness that governs gravitational behavior directly, without requiring extra mass. Balancing the inertial and compacity-gradient terms yields v(r) = rαβC0 rβ,(3) where αand βare empirically determined scaling constants and C0denotes the baseline compacity reference. This expression reproduces the observed rotation velocities across a wide range of galactic radii. Empirical Validation Application of this equation to the SPARC database (Spitzer Photometry and Accurate Rotation Curves) yields an aggregate correlation coefficient of R2≈0.997 across 80 representative galaxies. The fitting behavior remains consistent over multiple morphological types and mass scales, without the introduction of auxiliary matter parameters (Dark Matter). Interpretation and Implications •The flattening of galactic rotation curves results from the intrinsic field behavior of spacetime, not from unobserved matter. •Gravitational effects correspond to gradients in compacity (∇ρc), replacing curvature sourced by mass as the causal mechanism. •The model preserves energy conservation and remains compatible with lensing and redshift observations under the same formalism. Conclusion The rotation-curve anomaly, long attributed to hypothetical dark matter, finds a natural explanation in the Spacetime Compacity framework. By treating spacetime as a compressible field with variable density, SCT quantitatively reproduces observed galactic dynamics while eliminating the need for a made-up mass components. This result substantiates the viability of compacity as a fundamental property of the cosmos and positions SCT as a compelling successor to curvature-based gravitational interpretation. 2 Figures: Empirical scaling relationships derived from the SPARC galactic dataset, showing consistency with the Spacetime Compacity Gradient (SCG) formulation. Left: log(SCG) vs. log(Stellar Mass) indicates only weak dependence on total baryonic mass, demonstrating that compacity is not directly tied to luminous matter. Center: log(SCG) vs. log(Radius) shows a mild positive trend, reflecting increasing spatial gradient influence with galactocentric distance. Right: log(SCG) vs. log(Velocity) reveals a strong linear correlation, confirming that orbital velocity is governed by spacetime compacity rather than unseen mass. The shaded bands represent one–sigma uncertainty bounds of the regression fits. By treating spacetime as a compressible field with variable density, SCT quantitatively reproduces galactic dynamics without invoking hypothetical dark matter, establishing compacity as a fundamental physical property. References [1] Lelli, F., McGaugh, S., Schombert, J., and Pawlowski, M. (2016). The SPARC Database: Kinematics of 175 Disk Galaxies. Astronomical Journal, 152(6):157. [2] Davis, R. B., The Compacity of Spacetime, Kindle Books(2025). 3